$.)$ A random sample of $16$ size AA batteries for toys yield a mean of $3\mathrm{.}46$ hours with standard deviation, $0\mathrm{.}72$ hours.

$($a$)$ Find the critical value, $t^{***},$ for a $99\%Cl.t^{**}=$

$($b$)$ Find the margin of error for a $99\%Cl.$